Solve 5.r+7/2-2.r+4=3.x+9/4

$$\frac { 5 . r + 7 } { 2 } - 2 . r + 4 = \frac { 3 . x + 9 } { 4 }$$

Solve for r

$$r=\frac{3\left(x-7\right)}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(5r+7\right)-8r+16=3x+9$$

Use the distributive property to multiply 2 by 5r+7.

$$10r+14-8r+16=3x+9$$

Combine 10r and -8r to get 2r.

$$2r+14+16=3x+9$$

Add 14 and 16 to get 30.

$$2r+30=3x+9$$

Subtract 30 from both sides.

$$2r=3x+9-30$$

Subtract 30 from 9 to get -21.

$$2r=3x-21$$

Divide both sides by 2.

$$\frac{2r}{2}=\frac{3x-21}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$r=\frac{3x-21}{2}$$

Solve for x

$$x=\frac{2r}{3}+7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(5r+7\right)-8r+16=3x+9$$

Use the distributive property to multiply 2 by 5r+7.

$$10r+14-8r+16=3x+9$$

Combine 10r and -8r to get 2r.

$$2r+14+16=3x+9$$

Add 14 and 16 to get 30.

$$2r+30=3x+9$$

Swap sides so that all variable terms are on the left hand side.

$$3x+9=2r+30$$

Subtract 9 from both sides.

$$3x=2r+30-9$$

Subtract 9 from 30 to get 21.

$$3x=2r+21$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{2r+21}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{2r+21}{3}$$

Divide 2r+21 by 3.

$$x=\frac{2r}{3}+7$$